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A ball of mass (m) 0.5 kg is attached to...

A ball of mass (m) 0.5 kg is attached to the end of a string having length (L) 0.5 m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in radian/s) is:

Text Solution

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Consider the forces acting on the ball as shown in the figure.

`T cos theta` component will cancel mg.
`T sin theta` component will provide necessary cnetripetal force to the ball towards centre C.
`thereforeTsintheta=mromega^(2)=m(lsintheta)omega^(2)" or "T=mlomega^(2)`
`therefore"Angular velocity "omega=sqrt((T)/(ml))`
or `omega_("max")=sqrt((T_("max"))/(ml))=sqrt((324)/(0.5xx0.5))=36rads^(-1)`
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A ball of mass (m) 0.5kg is attached to the end of a string having length (L) 0.5m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324N. The maximum possible value of anguar velocity of ball(in radian/s) is

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Knowledge Check

  • A stone of mass 5 kg is tied to a string of length 10 m is whirled round in a horizontal circle. What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N?

    A
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    B
    `15 "ms"^(-1)`
    C
    `20 "ms"^(-1)`
    D
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